If AVG is removing the Logitech files to remove ATDMT then that is what is causing the damage and AdwCleaner may do a better job, but create another restore point and download/run it in Safe Mode with Networking which will keep AVG out of the picture (so to speak).

After thinking about it, I already use Skype. The Logitech is stopping Firefox from working. I wonder what would happen if I just uninstalled the Logitech program. To be honest, I use the laptop for calls and not the desktop.

If you are no longer using a program and it's causing a conflict then it's best to get rid of it.

I'm not sure what AVG has done with it but I would uninstall it intact with the infected files should any orphans be left and use a good 3rd party Uninstaller to dump it and then run your anti malware scan again - not forgetting MS's fixit to reset the Hosts file.